Creation Field Cosmological Model with Variable Cosmological Term (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>Λ</a:mi></a:math>) in Bianchi Type III Space-Time

The paper is devoted to the study of cosmological models with time-varying cosmological term ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"><a:mi>Λ</a:mi></a:math> ) in the presence of creation field in the framework of Bianchi type III space-time. To obtain deterministic model of the universe, we have assumed <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"><c:mi>Λ</c:mi><c:mo>∝</c:mo><c:mn>1</c:mn><c:mo>/</c:mo><c:msup><c:mrow><c:mi>R</c:mi></c:mrow><c:mrow><c:mn>3</c:mn></c:mrow></c:msup></c:math> , where <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M4"><e:mi>R</e:mi></e:math> is the scale factor, for steady state cosmology and creation field, and shear ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M5"><g:mi>σ</g:mi></g:math> ) is proportion to expansion ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M6"><i:mi>θ</i:mi></i:math> ) which leads to <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" id="M7"><k:mi>B</k:mi><k:mo>=</k:mo><k:msup><k:mrow><k:mi>C</k:mi></k:mrow><k:mrow><k:mi>n</k:mi></k:mrow></k:msup></k:math> , where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" id="M8"><m:mi>B</m:mi></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" id="M9"><o:mi>C</o:mi></o:math> are the metric potentials to explain small anisotropic behaviour of the universe and its isotropy. To obtain the results in terms of cosmic time <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" id="M10"><q:mi>t</q:mi></q:math> , we have assumed <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" id="M11"><s:mi>n</s:mi><s:mo>=</s:mo><s:mn>2</s:mn></s:math> . The model satisfies conservation equations, and creation field increases with time. The present model is free from singularity, has particle horizon, and provides a natural explanation for inflationary scenario and isotropization. Creation field and Einstein field equations are derived using principle of least action and Lagrangian formulation of variable cosmological term. For illustrative purposes, evolutionary behaviour of some cosmological parameters are shown graphically. The other physical aspects like accelerating behaviour of the model are also discussed. Thus, the model represents not only expanding universe but also accelerating which matches with the results of present-day observations.